Generalized decision feedback equalizer precoder with receiver beamforming for matrix calculations in multi-user multiple-input multiple-output wireless transmission systems

ABSTRACT

To realize a GDFE precoder for multi-user MIMO systems, which significantly reduces the computational cost while resulting in no capacity loss, one method comprises obtaining an effective downlink (DL) channel matrix H for the DL channel after receiver processing at the user terminals; computing an uplink (UL) covariance matrix D by assuming there are as many user terminals as a number of rows in the effective DL channel matrix H; computing a filter matrix C based on the UL covariance matrix D; computing a feedforward filter matrix F based on the filter matrix C; computing an interference pre-cancellation matrix G, based on the feedforward filter matrix F and the filter matrix C, used in a transmitter at an interference pre-cancellation stage of the GDFE precoder; and processing user symbols by a decision feedback equalizing stage of the GDFE precoder to produce filtered vector symbols.

RELATED APPLICATIONS

The present application is related to U.S. patent application Ser. No.12/401,711, filed Mar. 11, 2009, and concurrently filed U.S. patentapplication Ser. No. ______, (GENERALIZED DECISION FEEDBACK EQUALIZERPRECODER WITH INPUT COVARIANCE MATRIX CALCULATION FOR MULTI-USERMULTIPLE-INPUT MULTIPLE-OUTPUT WIRELESS TRANSMISSION SYSTEMS), theentire disclosures of which are incorporated herein by reference.

BACKGROUND OF THE INVENTION

The present invention relates generally to multiple-inputmultiple-output (MIMO) communications systems and, more particularly, toGeneralized Decision Feedback Equalizer (GDFE) based precoderconfiguration in MIMO systems and matrix calculations with receiverbeamforming.

It is well known that a Generalized Decision Feedback Equalizer (GDFE)based precoder provides the optimal capacity solution for Multi-userMultiple-Input Multiple-Output (MU-MIMO) wireless systems. However, thecomputational cost of determining various filters associated with theGDFE precoder is often prohibitive and is not suitable for manypractical systems.

There are several known preceding techniques which can enable a BaseStation (BS) equipped with multiple antennas to send simultaneous datastreams to multiple user terminals (UTs) in order to optimize systemcapacity. In general, preceding for a MU-MIMO system aims to optimize acertain criterion such as system capacity or bit error rate. Selectedreferences are noted below, together with a description of relevantaspects of the techniques proposed therein.

Q. H Spencer, A. L. Swindlehurst, and M. Haardt, “Zero-forcing methodsfor downlink spatial multiplexing in multi-user MIMO channels”, IEEETransactions on Signal Processing, pp. 461-471, February 2004 [1]describes a linear precoding technique, known as Block Diagonalization(BD), which separates out the data streams to different UTs by ensuringthat interference spans the Null Space of the victim UT's channel. TheBD technique diagonalizes the effective channel matrix so as to createmultiple isolated MIMO sub-channels between the BS and the UTs. Althoughthis scheme is simple to implement, it limits system capacity somewhat.

C. Windpassinger, R. F. H Fischer, T. Vencel, and J. B Huber, “Precodingin multi-antenna and multi-user communications”, IEEE Transactions onWireless Communications, pp. 1305-1316, July 2004 [2] describes anon-linear preceding scheme known as Tomlinson-Harashima Precoding(TIP). This scheme relies on successive interference pre-cancellation atthe BS. A modulo operation is used to ensure that transmit power is notexceeded. Different from BD and other linear techniques, THPtriangularizes the effective channel matrix and provides somewhat highersystem capacity when compared to BD and the like. However, it still doesnot provide the optimal system capacity.

In W. Yu, “Competition and Cooperation in Multi-User CommunicationEnvironments”, PhD Dissertation, Stanford University, February 2002 [3]and W. Yu and J. Cioffi, “Sum capacity of Gaussian vector broadcastchannels”, IEEE Transactions on Information Theory, pp. 1875-1892,September 2004 [4], Wei Yu introduced the GDFE precoder and showed thatit achieves a high degree of system capacity. The basic components ofthis scheme are illustrated in FIG. 1. The GDFE precoder includes aninterference pre-cancellation block 101. Similar to the THP precedingscheme discussed in reference [2] above, the interferencepre-cancellation helps to ensure that the symbol vector encoded at thek^(th) step will suffer from the interference from (k−1) symbol vectorsonly. Information symbols u are processed by the interferencepre-cancellation block 101 to produce filtered vector symbols x.

The filtered vector symbols x are then passed through a transmit filter103 denoted by matrix B to produce transmitted signals y. In reference[3] and [4], a technique based on the covariance matrix (S_(zz))corresponding to “Least Favorable Noise” is proposed to compute the GDFEprecoder components. Although, this technique achieves a high degree ofsystem capacity, the computational cost of determining the GDFE precodercomponents is effectively prohibitive for a real-time implementationrequired by most practical systems.

X. Shao, J. Yuan and P. Rapajic, “Precoder design for MIMO broadcastchannels”, IEEE International Conference on Communications (ICC), pp.788-794, May 2005 [5] proposes a different preceding technique whichachieves a capacity close to the theoretical maximum system capacity.The proposed method is computationally less complex compared to the GDFEprecoder technique. However, the proposed method allocates equal powerto all data streams, which may not be an effective technique forpractical systems using a finite number of quantized bit-rates. Also,the proposed technique is limited to invertible channel matrices, whichmay not always be the case.

N. Jindal, W. Rhee, S. Vishwanath, S. A. Jafar, and A. Goldsmith, “SumPower Iterative Water-filling for Multi-Antenna Gaussian BroadcastChannels”, IEEE Transactions on Information Theory, pp. 1570-1580, April2005 [6] derives a very useful result referred to as the MAC/BC(multiple access channel/broadcast channel) duality; and Wei Yu, DIMACSSeries in Discrete Mathematics and Theoretical Computer Science, Vol.66, “Advances in Network Information Theory,” pp. 159-171 [7] developsthe concept of least favorable noise.

The entire disclosures of the above references are incorporated hereinby reference.

BRIEF SUMMARY OF THE INVENTION

Exemplary embodiments of the invention provide a technique to realize aGDFE precoder for multi-user (MU) MIMO systems, which significantlyreduces the computational cost while resulting in no capacity loss. Thetechnique is suitable for improving the performance of various MU-MIMOwireless systems including presently planned future “4G” cellularnetworks. A computationally efficient framework is presented fordetermining various filters associated with the GDFE precoder in U.S.patent application Ser. No. 12/401,711. While it overcomes thecomputation complexity associated with the conventional GDFE precoder byreducing the computational cost without capacity loss, the feedbackoverhead associated with the GDFE precoder can still remain an issue.This invention focuses on the algorithm for reducing the feedbackoverhead while maintaining the advantages offered by that GDFE precoderdesign.

The present invention reduces the feedback overhead associated with thefeedforward filter F of the GDFE precoder. This is achieved byconditioning the downlink (DL) channel by means of receiver beamforming.The modified DL channel is then used to compute various matricesassociated with the GDFE filter assuming there exists no coordinationamong any receiver antennas for all users. This forces the feedforwardfilter F to be strictly diagonal, thus reducing the feedback overhead.Also, the channel conditioning using receiver beamforming ensures thatthe loss in capacity due to no coordination among receiver antennas isminimal.

An aspect of the present invention is directed to a method forprocessing user symbols with a generalized decision feedback equalizer(GDFE) based precoder in a base station of a multi-user multiple-inputmultiple-output (MU-MIMO) wireless system having K user terminals (UTs)which communicate with the base station via an uplink (UL) channel and acorresponding downlink (DL) channel. The method comprises obtaining aneffective downlink (DL) channel matrix H for the DL channel afterreceiver processing at the user terminals; computing an uplink (UL)covariance matrix D by assuming there are as many user terminals as anumber of rows in the effective DL channel matrix H, the UL covariancematrix D being a diagonal matrix; computing a filter matrix C based onthe UL covariance matrix D; computing a feedforward filter matrix Fbased on the filter matrix C; computing an interference pre-cancellationmatrix G, based on the feedforward filter matrix F and the filter matrixC, used in a transmitter at an interference pre-cancellation stage ofthe GDFE precoder; and processing user symbols by a decision feedbackequalizing stage of the GDFE precoder to produce filtered vectorsymbols. The effective downlink (DL) channel matrix is H=[Ĥ₁ ^(H), Ĥ₂^(H), . . . , Ĥ_(K) ^(H)], where Ĥ_(k) is an effective DL channelsub-matrix for the k^(th) UT Ĥ_(k)=S_(k)V_(k) ^(H), where S_(k) andV_(k) are matrices obtained from a singular value decomposition (SVD) ofan estimated DL channel matrix H_(k) for the k^(th) UT,H_(k)=U_(k)S_(k)V_(k) ^(H).

Another aspect of the invention is directed to a generalized decisionfeedback equalizer (GDFE) based precoder in a base station (BS) of amulti-user multiple-input multiple-output (MU-MIMO) wireless systemhaving K user terminals (UTs) which communicate with the base stationvia an uplink (UL) channel and a corresponding downlink (DL) channel.The GDFE precoder comprises a feedforward path; a feedback path; and aninterference pre-cancellation block denoted by I−G disposed in thefeedback path, I being an identity matrix, G being an interferencepre-cancellation matrix. The interference pre-cancellation matrix G iscomputed based on a feedforward filter matrix F and a filter matrix C,the feedforward filter matrix F is computed based on the filter matrixC, the filter matrix C is computed based on an uplink (UL) covariancematrix D, the UL covariance matrix D is computed by assuming there areas many user terminals as a number of rows in an effective downlink (DL)channel matrix H, the UL covariance matrix D is a diagonal matrix, andthe effective DL channel matrix H is obtained after receiver processingat the user terminals. The effective downlink (DL) channel matrix isH=[Ĥ₁ ^(H), Ĥ₂ ^(H), . . . , Ĥ_(K) ^(H)], where Ĥ_(k) is an effective DLchannel sub-matrix for the k^(th) UT, Ĥ_(k)=S_(k)V_(k) ^(H), where S_(k)and V_(k) are matrices obtained from a singular value decomposition(SVD) of an estimated DL channel matrix H_(k) for the k^(th) UT,H_(k)=U_(k)S_(k)V_(k) ^(H).

Another aspect of this invention is directed to a generalized decisionfeedback equalizer (GDFE) based precoder in a base station (BS) of amulti-user multiple-input multiple-output (MU-MIMO) wireless systemhaving K user terminals (UTs) which communicate with the base stationvia an uplink (UL) channel and a corresponding downlink (DL) channel.The GDFE precoder comprises a decision feedback equalizing stage forprocessing user symbols to produce filtered vector symbols, the decisionfeedback equalizing stage including an interference pre-cancellationstage having an interference pre-cancellation matrix G used in atransmitter at the interference pre-cancellation stage; and a transmitfilter represented by a transmit filter matrix B for processing thefiltered vector symbols after the decision feedback equalizing stage toproduce an output of transmitted signals to be directed to the DLchannel represented by the effective DL channel matrix H through whichcommunications occur in the wireless system with the user terminals. Theinterference pre-cancellation matrix G is computed based on afeedforward filter matrix F and a filter matrix C, the feedforwardfilter matrix F is computed based on the filter matrix C, the filtermatrix C is computed based on an uplink (UL) covariance matrix D, the ULcovariance matrix D is computed by assuming there are as many userterminals as a number of rows in an effective downlink (DL) channelmatrix H, the UL covariance matrix D is a diagonal matrix, and theeffective DL channel matrix H is obtained after receiver processing atthe user terminals. The effective downlink (DL) channel matrix is H=[Ĥ₁^(H), Ĥ₂ ^(H), . . . , Ĥ_(K) ^(H)], where H_(k) is an effective DLchannel sub-matrix for the k^(th) UT, Ĥ_(k)=S_(k)V_(k) ^(H), where S_(k)and V_(k) are matrices obtained from a singular value decomposition(SVD) of an estimated DL channel matrix H_(k) for the k^(th) UT,H_(k)=U_(k)S_(k)V_(k) ^(H).

These and other features and advantages of the present invention willbecome apparent to those of ordinary skill in the art in view of thefollowing detailed description of the specific embodiments.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram of a known GDFE precoder.

FIG. 2 is a block diagram of a communications system using GDFEpreceding.

FIG. 3 is a flow diagram of receiver processing according to anembodiment of the invention.

FIG. 4 is a flow diagram of GDFE precoder implementation according to anembodiment of the invention.

FIG. 5 is illustrates an example of a multi-user multiple-inputmultiple-output (MU-MIMO) wireless system showing a downlink channelrepresentation of a multi-antenna base station (BS) and multiple userterminals (UEs) according to an embodiment of the invention.

FIG. 6 illustrates an example of a communication block diagram for thedownlink information flow at the base station of FIG. 5.

DETAILED DESCRIPTION OF THE INVENTION

In the following detailed description of the invention, reference ismade to the accompanying drawings which form a part of the disclosure,and in which are shown by way of illustration, and not of limitation,exemplary embodiments by which the invention may be practiced. In thedrawings, like numerals describe substantially similar componentsthroughout the several views. Further, it should be noted that while thedetailed description provides various exemplary embodiments, asdescribed below and as illustrated in the drawings, the presentinvention is not limited to the embodiments described and illustratedherein, but can extend to other embodiments, as would be known or aswould become known to those skilled in the art. Reference in thespecification to “one embodiment”, “this embodiment”, or “theseembodiments” means that a particular feature, structure, orcharacteristic described in connection with the embodiment is includedin at least one embodiment of the invention, and the appearances ofthese phrases in various places in the specification are not necessarilyall referring to the same embodiment. Additionally, in the followingdetailed description, numerous specific details are set forth in orderto provide a thorough understanding of the present invention. However,it will be apparent to one of ordinary skill in the art that thesespecific details may not all be needed to practice the presentinvention. In other circumstances, well-known structures, materials,circuits, processes and interfaces have not been described in detail,and/or may be illustrated in block diagram form, so as to notunnecessarily obscure the present invention.

Furthermore, some portions of the detailed description that follow arepresented in terms of algorithms and symbolic representations ofoperations within a computer. These algorithmic descriptions andsymbolic representations are the means used by those skilled in the dataprocessing arts to most effectively convey the essence of theirinnovations to others skilled in the art. An algorithm is a series ofdefined steps leading to a desired end state or result. In the presentinvention, the steps carried out require physical manipulations oftangible quantities for achieving a tangible result. Usually, though notnecessarily, these quantities take the form of electrical or magneticsignals or instructions capable of being stored, transferred, combined,compared, and otherwise manipulated. It has proven convenient at times,principally for reasons of common usage, to refer to these signals asbits, values, elements, symbols, characters, terms, numbers,instructions, or the like. It should be borne in mind, however, that allof these and similar terms are to be associated with the appropriatephysical quantities and are merely convenient labels applied to thesequantities. Unless specifically stated otherwise, as apparent from thefollowing discussion, it is appreciated that throughout the description,discussions utilizing terms such as “processing”, “computing”,“calculating”, “determining”, “displaying”, or the like, can include theactions and processes of a computer system or other informationprocessing device that manipulates and transforms data represented asphysical (electronic) quantities within the computer system's registersand memories into other data similarly represented as physicalquantities within the computer system's memories or registers or otherinformation storage, transmission or display devices.

The present invention also relates to an apparatus for performing theoperations herein. This apparatus may be specially constructed for therequired purposes, or it may include one or more general-purposecomputers selectively activated or reconfigured by one or more computerprograms. Such computer programs may be stored in a computer-readablestorage medium, such as, but not limited to optical disks, magneticdisks, read-only memories, random access memories, solid state devicesand drives, or any other types of media suitable for storing electronicinformation. The algorithms and displays presented herein are notinherently related to any particular computer or other apparatus.Various general-purpose systems may be used with programs and modules inaccordance with the teachings herein, or it may prove convenient toconstruct a more specialized apparatus to perform desired method steps.In addition, the present invention is not described with reference toany particular programming language. It will be appreciated that avariety of programming languages may be used to implement the teachingsof the invention as described herein. The instructions of theprogramming language(s) may be executed by one or more processingdevices, e.g., central processing units (CPUs), processors, orcontrollers.

Exemplary embodiments of the invention, as will be described in greaterdetail below, provide apparatuses, methods and computer programs forGDFE precoder configuration in MIMO systems and matrix calculations withreceiver beamforming.

A. System Model

First, the system, model and notations used herein are set forth. Letthe base station (BS) have N_(t) antennas and let there be K userterminals (UTs) with L_(k) antennas each. The sum of antennas at all UTsis denoted as L=Σ_(k=1) ^(K)L_(k). Let H_(k) denote the channel gainmatrix of dimensions {L_(k)×N_(k)} between the BS and the k^(th) UT. Thecombined channel gain matrix between the BS and the K UTs is ofdimension {L×N_(t)} and is given by H=[H₁ ^(T)H₂ ^(T) . . . H_(K)^(T)]^(T), where the superscript ^(T) denotes the matrix transpose.

Let u_(k) denote the input symbol vector destined for the k^(th) UT, sothat the stacked input vector can be represented as u=[u₁ ^(T)u₂ ^(T) .. . u_(K) ^(T)]^(T). The length of u is assumed not to exceed the numberof antennas at the BS. Also, assume the additional constraint thatS_(uu)=E[uu^(H)]=I, where E[.] indicates the time average of itsargument, the superscript H denotes the conjugate transpose and Idenotes the identity matrix.

A. 1 Definitions

Referring to FIG. 2, a functional block diagram is shown of a MU-MIMOsystem having a base station 210 and user terminals 220 ₁-220 _(k). Eachuser terminal has associated therewith a feedforward filter F₁-F_(K).Communications occur through a channel 231 represented by a channelmatrix H. The base station includes a GDFE precoder including afeedforward path and a feedback path. In the feedforward path, a modulounit 233 produces a stream of filtered vector symbols X, which arefiltered by a transmit filter 235 to produce a transmitted signal streamy. In the feedback path, the symbols X are fed back through aninterference pre-cancellation block 237, represented by an interferencepre-cancellation matrix G subtracted from the identity matrix I. Astream of user symbols u has subtracted therefrom an output signal ofthe interference pre-cancellation block 237, with the result beingapplied to the modulo unit 233.

Other aspects/parameters related to this system model are describedbelow:

1). Interference Pre-Cancellation Matrix (G): This matrix is used at thetransmitter at Interference Pre-cancellation Stage of the GDFE precoderas shown in FIG. 2. The main purpose of this matrix is to process inputsymbol vector u for interference pre-cancellation purposes. Itsstructure is that of an Upper Right Triangular matrix with blockdiagonal sub-matrices being identity matrices each of size a_(k).

2). Input Covariance Matrix for Downlink Channel (S_(xx)): It is definedas S_(xx)=E[xx^(H)] and satisfies the transmit power constraint, i.e.,trace(S_(xx))≦P_(t), where P_(t) denotes the total available transmitpower and trace(.) indicates the sum of diagonal elements of the matrixargument. The input covariance matrix for the downlink channelrepresents dependencies of symbols transmitted from different ones ofsaid N_(t) transmit antennas; a sum of diagonal matrix elementsrepresents an intended total transmit power from the N_(t) transmitantennas. In the following text, S_(xx) will be represented using itsEigen Value Decomposition (EVD) as:

S_(xx)=VΣV^(H)   (1)

where V is a unitary matrix and Σ is a diagonal matrix with non-negativeentries.

3). Transmit Filter (B): This matrix is used to process the symbolvector x obtained after the DFE stage of GDFE precoder as shown in FIG.2. It is denoted by the following equation:

B=VΣ^(1/2)M   (2)

where M is a unitary matrix and the matrices {V, Σ} are same as definedin (1).

4). Least Favorable Noise Covariance Matrix (S_(zz)): This may beregarded as the noise covariance matrix that results in the minimumsystem capacity when full coordination among all UTs is assumed. This isa positive definite Hermitian Matrix whose block diagonal sub-matricesare identity matrices of size a_(k). This is defined in a similarfashion to that shown in Eq. (67) of the Yu and Cioffi reference [4].

5). Input Covariance Matrix for Equivalent Uplink Channel (D): It isdefined similar to the Equation (3.6) of reference [7] as thecorrelation among the symbols of the input vector for the equivalentUplink/Medium Access Channel (MAC) with channel matrix H^(H). Thestructure of matrix D is that of a block diagonal matrix and satisfiesthe transmit power constraint, i.e., trace( D)≦P_(t), where P_(t)denotes the total available transmit power. Each block diagonalsub-matrix of D represents the input covariance matrix for a particularUT in the Uplink channel. A capacity optimal D can be computed using themethodology presented in reference [6].

A.2 Transmitter Processing

As shown in FIG. 2, the GDFE precoder includes an interferencepre-cancellation block denoted by I−G , where G has the structure of aBlock Upper Right Triangular matrix. Similar to the THP precoding schemeof reference [2], the triangular structure of the feedback matrix Ghelps to ensure that the symbol vector encoded at the k^(th) step willsuffer from the interference from (k−1) symbol vectors only. The x_(k)^(th) sub-vector of x=[x₁ ^(T)x₂ ^(T) . . . x_(K) ^(T)]^(T) is generatedusing the following relationship:

$\begin{matrix}{x_{k} = {\left( {u_{k} - {\sum\limits_{m = {k + 1}}^{K}{G_{km}x_{m}}}} \right) + \alpha_{k}}} & (3)\end{matrix}$

where G_(km) denotes the sub-matrix of G required to pre-cancelinterference due to the vector symbol x_(m) from x_(k). Thesesub-vectors are generated in the reverse order, with x_(k) being thefirst generated vector and x_(i) being the last one. An example of thestructure of the matrix G for a 3 UT scenario is shown below

$\begin{matrix}{G = \begin{bmatrix}I & G_{12} & G_{13} \\0 & I & G_{23} \\0 & 0 & I\end{bmatrix}} & (4)\end{matrix}$

In this particular example, x₃ is generated first, followed by x₂ fromwhich interference due to x₃ is pre-subtracted using the sub-matrix G₂₃.Lastly, x₁ is generated after pre-subtraction of interference due to x₂and x₃. Also, each complex element of vector α_(k) in (3) is chosen fromthe following set:

A={2√{square root over (S)}(p ₁ +jp _(Q))|p ₁ , p _(Q)ε{±1, ±3, . . . ,±(√{square root over (S)}−1)}},   (5)

-   -   where S is the constellation size.

The elements of α_(k) are chosen such that the elements of the resultingvector x_(k) are bounded by the square region of width 2√{square rootover (S)}. This mechanism, while allowing for interferencepre-cancellation, also limits the total transmit power.

The vector x is then passed through a transmit filter B to yield avector y given by the following relationship:

y=Bx   (6)

The vector y is transmitted by mapping its element to the respectiveantenna elements of the Base Station.

B. Receiver Processing

FIG. 3 is a flow diagram of receiver processing. Each UT will determinethe corresponding DL channel associated with the BS. Let H_(k) denotethe estimated DL channel matrix for the k^(th) UT (step 302). The UTwill perform singular value decomposition (SVD) in step 304 as:

H_(k)=U_(k)S_(k)V_(k) ^(H)   (7)

where U_(k) denotes left singular vectors, S_(k) is a diagonal matrixwith singular values making up the diagonal, and V_(k) denotes the rightsingular vectors.

It is proposed that the UT employ U_(k) ^(H) for receiver processing andinform the BS of the following estimated channel (step 306):

Ĥ_(k)=S_(k)V_(k) ^(H)   (8)

Let the feedforward filter (computed by BS and passed to each UT)employed by k^(th) UT be denoted by F_(k) (step 308), which is a matrixof dimension {a_(k)×L_(k)} where a_(k) denotes the length of vectoru_(k). Now, the baseband vector corresponding to the data for k^(th) UTcan be estimated as

r _(k) =F _(k) U _(k) ^(H)(HBx+n _(k))   (9)

where x is the symbol vector derived from the input symbol vector uafter the interference pre-cancellation step as shown in FIG. 1. Thefilter B indicates the power covariance matrix and the noise at thek^(th) UT is denoted by n_(k). The feedforward filter F_(k) is strictlydiagonal. In step 310, the receiver processing matrix is computed asF_(k)U_(k) ^(H). In step 312, the incoming data vector r_(k) isprocessed to retrieve the transmitted baseband vector as {tilde over(x)}_(k)=F_(k)U_(k) ^(H)r_(k).

B. Transmitter Processing and Computation of GDFE Precoder Matrices

FIG. 4 is a flow diagram of GDFE precoder implementation. In step 402,the program gets the effective DL channel after receiver processing (seeFIG. 3). The effective DL channel matrix can be represented as:

H=[Ĥ₁ ^(H), Ĥ₁ ^(H), . . . , Ĥ_(k) ^(H)]  (10)

where Ĥ_(k) is a sub-matrix that corresponds to the effective DL channelfor the k^(th) UT as given in (8). In step 404, we compute the optimalUplink Covariance Matrix, D, assuming there exist as many UTs as thenumber of the rows in the channel matrix H. This is a key condition andit implies that no coordination is assumed among any of the receiverantennas at all UTs. The algorithms in [6] or concurrently filed U.S.patent application Ser. No. ______, referenced above can be used tocompute D. Here it must be noted that the imposed condition of “nocoordination among receiver antennas” on D ensures that it is a strictlydiagonal matrix.

In step 406, we compute the corresponding Input Covariance Matrix forthe DL channel (S_(xx)). The reference [7] provides the followingrelation between input covariance matrices of the UL and correspondingDL channels as:

$\begin{matrix}{S_{xx} = {{V\; \Sigma \; V^{H}} = \frac{I - \left\lbrack {{H_{DL}^{H}{DH}_{DL}} + I} \right\rbrack^{- 1}}{\lambda}}} & (11)\end{matrix}$

where, λ denotes the UL/DL duality variable as defined in [7] and can becomputed as

λ=trace(I−[H _(DL) ^(H) DH _(DL) +I] ⁻¹)/P _(t)   (12)

In step 408, we follow the development in U.S. patent application Ser.No. 12/401,711 to compute the filter matrix C:

C=[√{square root over (Σ^(†))}−λ√{square root over (Σ)}]V ^(H) H ^(H) D  (13)

In step 410, let C=MR denote the QR decomposition (QRD) of C, where M isunitary matrix and R is an upper right triangular matrix. Now variousGDFE related matrices (transmit filter B, feedback filter G, andfeedforward filter F) can be computed as follows. In step 412, theprogram computes the transmit filter B

B=VΣ^(1/2)M   (14)

In step 414, we extract sub-matrices F₁, F₂, . . . , F_(K) from thediagonals of R and send them to all the UTs.

F=Diagonal(R).   (15)

In step 416, the program computes the feedback matrix G

G=FR^(\)  (16)

where the superscript \ denotes the Moore-Penrose Generalized Inverse.

The BS informs each UT of the corresponding submatrices F₁, F₂ . . . ,F_(K) required for receiver processing.

C. Numerical Example

The following numerical example illustrates the computation of variousmatrices involved in the design of GDFE precoder of the presentinvention. Consider a BS with 4 antennas and 2 users with 2 antennaseach, so that the channel matrices associated with both of the users areof dimension 2×4. The transmit power is assumed to be 20. For the sakeof simplicity, we consider a real channel as follows:

$\quad\begin{matrix}\begin{matrix}{H = \begin{bmatrix}H_{1} \\H_{2}\end{bmatrix}} \\{= \begin{bmatrix}0.8861 & 0.3159 & {- 0.3873} & 0.0470 \\0.3418 & 0.5586 & 1.1395 & {- 1.5820} \\1.6312 & {- 0.1095} & {- 1.3211} & 0.0545 \\1.1802 & {- 1.3143} & 0.5873 & 1.2575\end{bmatrix}}\end{matrix} & (17)\end{matrix}$

Next, we compute the SVD decomposition of H₁ and H₂ as follows

$\begin{matrix}{{H_{1} = {\underset{\underset{U_{1}}{}}{\begin{bmatrix}{- 0.0113} & 0.9999 \\0.9999 & 0.0113\end{bmatrix}}\underset{\underset{S_{1}}{}}{\begin{bmatrix}2.0568 & 0 & 0 & 0 \\0 & 1.0182 & 0 & 0\end{bmatrix}}{\underset{\underset{V_{1}^{H}}{}}{\begin{bmatrix}0.1613 & 0.8740 & 0.4407 & {- 0.1260} \\0.2698 & 0.3164 & {- 0.5113} & 0.7521 \\0.5561 & {- 0.3676} & 0.6365 & 0.3879 \\{- 0.7694} & 0.0285 & 0.3731 & 0.5177\end{bmatrix}}}^{H}\mspace{14mu} {and}}},} & (18) \\{H_{2} = {\underset{\underset{U_{2}}{}}{\begin{bmatrix}{- 0.6229} & {- 0.7823} \\{- 0.7823} & 0.6229\end{bmatrix}}\underset{\underset{S_{2}}{}}{\begin{bmatrix}2.4761 & 0 & 0 & 0 \\0 & 1.8267 & 0 & 0\end{bmatrix}}{\underset{\underset{V_{2}^{H}}{}}{\begin{bmatrix}{- 0.7832} & {- 0.2961} & 0.5332 & {- 0.1208} \\0.4428 & {- 0.4013} & 0.5580 & 0.5757 \\0.1468 & 0.7660 & 0.6039 & {- 0.1642} \\{- 0.4110} & 0.4055 & {- 0.1992} & 0.7918\end{bmatrix}}}^{H}}} & (19)\end{matrix}$

Now, the effective channels after the proposed receiver processing byU_(k) ^(H) for the two users are

$\begin{matrix}{{{\hat{H}}_{1} = {{U_{1}^{H}H_{1}} = \begin{bmatrix}0.3317 & 0.5550 & 1.1438 & {- 1.5824} \\0.8899 & 0.3222 & {- 0.3743} & 0.0290\end{bmatrix}}}{{and},}} & (20) \\{{\hat{H}}_{2} = {{U_{2}^{H}H_{2}} = \begin{bmatrix}{- 1.9393} & 1.0964 & 0.3634 & {- 1.0177} \\{- 0.5409} & {- 0.7331} & 1.3993 & 0.7407\end{bmatrix}}} & (21)\end{matrix}$

Thus, the overall effective downlink channel is given by

$\quad\begin{matrix}\begin{matrix}{\hat{H} = \left\lbrack {{\hat{H}}_{1}^{H},{\hat{H}}_{2}^{H}} \right\rbrack^{H}} \\{= \begin{bmatrix}0.3317 & 0.5550 & 1.1438 & {- 1.5824} \\0.8899 & 0.3222 & {- 0.3743} & 0.0290 \\{- 1.9393} & 1.0964 & 0.3634 & {- 1.0177} \\{- 0.5409} & {- 0.7331} & 1.3993 & 0.7407\end{bmatrix}}\end{matrix} & (22)\end{matrix}$

Next, we compute the power covariance matrix D for the equivalent MACchannel assuming there exist as many UTs as the number of the rows inthe effective channel matrix Ĥ (i.e., 4). The solution can be foundusing the algorithm in reference [6] which converges in four iterations

$\begin{matrix}{D = \begin{bmatrix}6.3049 & 0 & 0 & 0 \\0 & 1.2059 & 0 & 0 \\0 & 0 & 6.3225 & 0 \\0 & 0 & 0 & 6.1668\end{bmatrix}} & (23)\end{matrix}$

Now, for the given transmit power of 20, the optimal transmit powercovariance matrix S_(xx) can be computed using equation (11) as

$\begin{matrix}{S_{xx} = \begin{bmatrix}6.0853 & {- 0.9522} & {- 0.3370} & {- 0.5316} \\{- 0.9522} & 2.9716 & {- 1.0238} & {- 2.2041} \\{- 0.3370} & {- 1.0238} & 5.9656 & {- 0.6997} \\{- 0.5316} & {- 2.2041} & {- 0.6997} & 4.9775\end{bmatrix}} & (24)\end{matrix}$

The Eigen Value Decomposition (EVD) S_(xx)=VΣV^(H) can be computed as

$\begin{matrix}{{V = \begin{bmatrix}{- 0.2175} & {- 0.5482} & 0.5784 & 0.5636 \\{- 0.7942} & 0.4463 & 0.3448 & {- 0.2263} \\{- 0.2491} & 0.3330 & {- 0.5111} & 0.7522 \\{- 0.5098} & {- 0.6241} & {- 0.5342} & {- 0.2555}\end{bmatrix}}{and}} & (25) \\{\Sigma = \begin{bmatrix}0.9750 & 0 & 0 & 0 \\0 & 6.4599 & 0 & 0 \\0 & 0 & 6.3064 & 0 \\0 & 0 & 0 & 6.2587\end{bmatrix}} & (26)\end{matrix}$

Next, we compute the matrix C and its QR Decomposition as

$\begin{matrix}{\mspace{79mu} \begin{matrix}{C = {\left\lbrack {\sqrt{\Sigma^{\dagger}} - {\lambda \sqrt{\Sigma}}} \right\rbrack V^{H}{\hat{H}}^{H}D}} \\{{= \begin{bmatrix}0.0483 & {- 0.3861} & {- 0.1131} & {- 0.1400} \\0.0742 & {- 0.0048} & 0.1198 & {- 0.0014} \\0.0713 & 0.0170 & {- 0.0429} & {- 0.1817} \\0.1716 & 0.0035 & {- 0.1048} & 0.0917\end{bmatrix}}\;}\end{matrix}} & (27) \\{C = {\underset{\underset{M}{}}{\begin{bmatrix}0.2346 & {- 0.9712} & {- 0.0215} & {- 0.0366} \\0.3604 & 0.0670 & 0.9303 & {- 0.0146} \\0.3465 & 0.1217 & {- 0.1574} & {- 0.9167} \\0.8337 & 0.1938 & {- 0.3307} & 0.3976\end{bmatrix}\quad}\underset{\underset{R}{}}{\quad\begin{bmatrix}0.2059 & {- 0.0836} & {- 0.0856} & {- 0.0198} \\0 & 0.3773 & 0.0923 & 0.1316 \\0 & 0 & 0.1552 & 0 \\0 & 0 & 0 & 0.2081\end{bmatrix}}}} & (28)\end{matrix}$

Now, the transmit filter B is computed as

$\quad\begin{matrix}\begin{matrix}{B = {V\; \Sigma^{1/2}M}} \\{= \begin{bmatrix}1.1264 & 0.5652 & {- 1.9863} & {- 0.7427} \\0.0529 & 0.8334 & 1.1229 & {- 1.0067} \\1.3715 & 0.5040 & 0.3722 & 1.9215 \\{- 1.6874} & 0.0954 & {- 1.0424} & 1.0171\end{bmatrix}}\end{matrix} & (29)\end{matrix}$

The effective feedforward filter can be computed as

$\quad\begin{matrix}\begin{matrix}{F = \begin{bmatrix}F_{1} & 0 \\0 & F_{2}\end{bmatrix}} \\{= {{diag}(R)}} \\{= \begin{bmatrix}0.2059 & 0 & 0 & 0 \\0 & 0.3773 & 0 & 0 \\0 & 0 & 0.1552 & 0 \\0 & 0 & 0 & 0.2081\end{bmatrix}}\end{matrix} & (30)\end{matrix}$

Therefore, the two users employ the following feedforward filters forbaseband signal processing

$\begin{matrix}{{F_{1} = \begin{bmatrix}0.2059 & 0 \\0 & 0.3773\end{bmatrix}},{F_{2} = \begin{bmatrix}0.1552 & 0 \\0 & 0.2081\end{bmatrix}}} & (31)\end{matrix}$

The interference pre-cancellation matrix G can be computed as

$\quad\begin{matrix}\begin{matrix}{G = {FR}^{- 1}} \\{= \begin{bmatrix}1 & 0.2214 & 0.4199 & {- 0.0446} \\0 & 1 & {- 0.5945} & {- 0.6321} \\0 & 0 & 1 & 0 \\0 & 0 & 0 & 1\end{bmatrix}}\end{matrix} & (32)\end{matrix}$

D. Wireless Transmission System

FIG. 5 is illustrates an example of a multi-user multiple-inputmultiple-output (MU-MIMO) wireless system showing a downlink channelrepresentation of a multi-antenna base station (BS) and multiple userterminals (UEs) according to an embodiment of the invention.

D.1 Channel Matrix Definition

The downlink channel between a base station (BS) and several userterminals (UEs) is normally represented as a matrix H whose number ofrows equals to the sum of antennas at the UEs and number of columns isthe same as the number of transmit antennas at the BS. The (i,j)^(th)entry represents the complex channel gain h_(ij) between the i^(th)transmit antenna and j^(th) receive antenna as shown in FIG. 5. Inparticular, complex channel gain h_(ij) represents the amplification (orattenuation) that a transmitted signal undergoes in the wirelesschannel.

D.2 Channel Matrix Estimation

In a Frequency Division Duplex (FDD) system such as OFDMA, the complexchannel gain h_(ij) is usually estimated at the UE end. The channelestimation process is as follows. First, at the BS, antenna #1 transmitsa reference signal. All the UEs estimate the received signal at eachreceiver antenna. As the reference signal is known to all UEs, thechannel gain corresponding to the 1^(st) transmit antenna can bedetermined (assuming noise level is sufficiently below the referencesignal power). This procedure is then repeated for transmit antennasnumber 2 to N_(t).

In this way, the channel matrix H_(k) corresponding to the k^(th) UE canbe estimated. Afterwards, all the UEs report back their respectivechannels to the BS using a dedicated feedback channel. The BS can thencoalesce individual channel matrices to obtain the overall channelmatrix H.

In Time Division Duplex (TDD) systems, the channel matrix can beestimated at the BS exploiting channel reciprocity property (i.e., ULand DL channels are related by some mathematical expression). For suchsystems, at a given time, one of the UEs will transmit a referencesignal using a given antenna. This signal is captured by all theantennas at the BS and thus the corresponding channel gains are known.This process is repeated by all the UEs for all the available antennas,resulting in the estimate of complete Uplink channel matrix. The BS canthen use some mathematical transformation (such as complex conjugation)to obtain equivalent downlink channel.

D.3 Information Flow from Base Station to User Terminals

FIG. 6 illustrates an example of a communication block diagram for thedownlink information flow at the base station of FIG. 5. The informationto be sent to different UEs is represented by different codewords (oneor more codewords can be assigned to a single UE). The bits in a givencodeword are then scrambled using a predetermined scrambling code(Scrambling block) which is known both at the BS and UEs. The scrambledbits are then mapped (Modulation Mapper block) to a complex modulationsymbol (e.g., BPSK, QPSK, QAM, etc.). These information symbols are thenmapped (Layer Mapper block) to Layers (a stream of complex symbols) asshown in FIG. 6. The number of Layers is usually less than or equal tothe rank of the channel matrix H. The information symbols mapped todifferent Layers are then processed in a Precoding block (whichimplements GDFE or THP etc). The precoded symbols are then mapped toresource elements within a Resource Element Mapper block (which is arectangular grid of OFDM tones and time slots). These symbols are thenfed to an OFDM Signal Generator and the output is mapped to the transmitantenna ports.

The computers and storage systems implementing the invention can alsohave known I/O devices (e.g., CD and DVD drives, floppy disk drives,hard drives, etc.) which can store and read the modules, programs anddata structures used to implement the above-described invention. Thesemodules, programs and data structures can be encoded on suchcomputer-readable media. For example, the data structures of theinvention can be stored on computer-readable media independently of oneor more computer-readable media on which reside the programs used in theinvention. The components of the system can be interconnected by anyform or medium of digital data communication, e.g., a communicationnetwork. Examples of communication networks include local area networks,wide area networks, e.g., the Internet, wireless networks, storage areanetworks, and the like.

In the description, numerous details are set forth for purposes ofexplanation in order to provide a thorough understanding of the presentinvention. However, it will be apparent to one skilled in the art thatnot all of these specific details are required in order to practice thepresent invention. It is also noted that the invention may be describedas a process, which is usually depicted as a flowchart, a flow diagram,a structure diagram, or a block diagram. Although a flowchart maydescribe the operations as a sequential process, many of the operationscan be performed in parallel or concurrently. In addition, the order ofthe operations may be re-arranged.

As is known in the art, the operations described above can be performedby hardware, software, or some combination of software and hardware.Various aspects of embodiments of the invention may be implemented usingcircuits and logic devices (hardware), while other aspects may beimplemented using instructions stored on a machine-readable medium(software), which if executed by a processor, would cause the processorto perform a method to carry out embodiments of the invention.Furthermore, some embodiments of the invention may be performed solelyin hardware, whereas other embodiments may be performed solely insoftware. Moreover, the various functions described can be performed ina single unit, or can be spread across a number of components in anynumber of ways. When performed by software, the methods may be executedby a processor, such as a general purpose computer, based oninstructions stored on a computer-readable medium. If desired, theinstructions can be stored on the medium in a compressed and/orencrypted format.

From the foregoing, it will be apparent that the invention providesmethods, apparatuses and programs stored on computer readable media forGDFE precoder configuration in MIMO systems and matrix calculations withreceiver beamforming. Additionally, while specific embodiments have beenillustrated and described in this specification, those of ordinary skillin the art appreciate that any arrangement that is calculated to achievethe same purpose may be substituted for the specific embodimentsdisclosed. This disclosure is intended to cover any and all adaptationsor variations of the present invention, and it is to be understood thatthe terms used in the following claims should not be construed to limitthe invention to the specific embodiments disclosed in thespecification. Rather, the scope of the invention is to be determinedentirely by the following claims, which are to be construed inaccordance with the established doctrines of claim interpretation, alongwith the full range of equivalents to which such claims are entitled.

1. A method for processing user symbols with a generalized decisionfeedback equalizer (GDFE) based precoder in a base station of amulti-user multiple-input multiple-output (MU-MIMO) wireless systemhaving K user terminals (UTs) which communicate with the base stationvia an uplink (UL) channel and a corresponding downlink (DL) channel,the method comprising: obtaining an effective downlink (DL) channelmatrix H for the DL channel after receiver processing at the userterminals; computing an uplink (UL) covariance matrix D by assumingthere are as many user terminals as a number of rows in the effective DLchannel matrix H, the UL covariance matrix D being a diagonal matrix;computing a filter matrix C based on the UL covariance matrix D;computing a feedforward filter matrix F based on the filter matrix C;computing an interference pre-cancellation matrix G, based on thefeedforward filter matrix F and the filter matrix C, used in atransmitter at an interference pre-cancellation stage of the GDFEprecoder; and processing user symbols by a decision feedback equalizingstage of the GDFE precoder to produce filtered vector symbols; whereinthe effective downlink (DL) channel matrix isH=[Ĥ₁ ^(H), Ĥ₂ ^(H), . . . , Ĥ_(k) ^(H)], where Ĥ_(k) is an effective DLchannel sub-matrix for the k^(th) UTĤ_(k)=S_(k)V_(k) ^(H), where S_(k) and V_(k) are matrices obtained froma singular value decomposition (SVD) of an estimated DL channel matrixH_(k) for the k^(th) UTH_(k)=U_(k)S_(k)V_(k) ^(H).
 2. The method of claim 1, wherein U_(k) ^(H)is used for receiver processing at the k^(th) UT and the effective DLchannel sub-matrix for the k^(th) UT, Ĥ_(k), is provided to the basestation by the k^(th) UT.
 3. The method of claim 1, whereinC=[√{square root over (Σ^(†))}−λ√{square root over (Σ)}]V ^(H) H ^(H) D,where superscript † denotes a Moore-Penrose Generalized Inverse, andwhere V is a unitary matrix and Σ is a diagonal matrix with non-negativeentries in an Eigen Value Decomposition (EVD) of an input covariancematrix S_(xx) represented asS_(xx)=VΣV^(H), and λ is a UL/DL duality variable for a given totaltransmit power P_(t),λ=trace(I−[H _(DL) ^(H) DH _(DL) +I] ⁻¹)/P _(t), where V is a unitarymatrix and Σ is a diagonal matrix with non-negative entries, and theinput covariance matrix S_(xx) is computed as$S_{xx} = {{V\; \Sigma \; V^{H}} = {\frac{I - \left\lbrack {{H_{DL}^{H}{DH}_{DL}} + I} \right\rbrack^{- 1}}{\lambda}.}}$4. The method of claim 3, wherein C=MR denotes QR decomposition (QRD) ofC, M being a unitary matrix, and R being an upper right triangularmatrix; wherein the feedforward filter matrix F isF=Diagonal(R); and wherein the interference pre-cancellation matrix G isG=FR^(†), where superscript † denotes a Moore-Penrose GeneralizedInverse.
 5. The method of claim 4, further comprising: computing atransmit filter matrix B for a transmit filterB=VΣ^(1/2)M; passing the filtered vector symbols through the transmitfilter to produce an output of transmitted signals; directing the outputof the transmit filter to the channel represented by the effective DLchannel matrix H through which communications occur in the wirelesssystem with the user terminals.
 6. The method of claim 1, whereinprocessing user symbols by a decision feedback equalizing stage of theGDFE precoder to produce filtered vector symbols comprises: directingthe user symbols through a modulo unit disposed in a feedforward path toproduce the filtered vector symbols which are fed back through aninterference pre-cancellation block disposed in a feedback path, theinterference pre-cancellation block being denoted by I−G; andsubtracting an output signal of the interference pre-cancellation blockfrom the user symbols which are applied to the modulo unit in thefeedforward path.
 7. A generalized decision feedback equalizer (GDFE)based precoder in a base station (BS) of a multi-user multiple-inputmultiple-output (MU-MIMO) wireless system having K user terminals (UTs)which communicate with the base station via an uplink (UL) channel and acorresponding downlink (DL) channel, the GDFE precoder comprising: afeedforward path; a feedback path; and an interference pre-cancellationblock denoted by I−G disposed in the feedback path, I being an identitymatrix, G being an interference pre-cancellation matrix; wherein theinterference pre-cancellation matrix G is computed based on afeedforward filter matrix F and a filter matrix C, the feedforwardfilter matrix F is computed based on the filter matrix C, the filtermatrix C is computed based on an uplink (UL) covariance matrix D, the ULcovariance matrix D is computed by assuming there are as many userterminals as a number of rows in an effective downlink (DL) channelmatrix H, the UL covariance matrix D is a diagonal matrix, and theeffective DL channel matrix H is obtained after receiver processing atthe user terminals; wherein the effective downlink (DL) channel matrixisH=[Ĥ₁ ^(H), Ĥ₂ ^(H), . . . , Ĥ_(K) ^(H)] where Ĥ_(k) is an effective DLchannel sub-matrix for the k^(th) UTĤ_(k)=S_(k)V_(k) ^(H) where S_(k) and V_(k) are matrices obtained from asingular value decomposition (SVD) of an estimated DL channel matrixH_(k) for the k^(th) UTH_(k)=U_(k)S_(k)V_(k) ^(H).
 8. The GDFE precoder of claim 7, whereinU_(k) ^(H) is used for receiver processing at the k^(th) UT and theeffective DL channel sub-matrix for the k^(th) UT, Ĥ_(k), is provided tothe base station by the k^(th) UT.
 9. The GDFE precoder of claim 7,whereinC=[√{square root over (Σ^(†))}−λ√{square root over (Σ)}]V ^(H) H ^(H) D,where superscript † denotes a Moore-Penrose Generalized Inverse, andwhere V is a unitary matrix and Σ is a diagonal matrix with non-negativeentries in an Eigen Value Decomposition (EVD) of an input covariancematrix S_(xx) represented asS_(xx)=VΣV^(H), and λ is a UL/DL duality variable for a given totaltransmit power P_(t),λ=trace(I−[H _(DL) ^(H) DH _(DL) +I]⁻¹)/P _(t), where V is a unitarymatrix and Σ is a diagonal matrix with non-negative entries, and theinput covariance matrix S_(xx) is computed as$S_{xx} = {{V\; \Sigma \; V^{H}} = {\frac{I - \left\lbrack {{H_{DL}^{H}{DH}_{DL}} + I} \right\rbrack^{- 1}}{\lambda}.}}$10. The GDFE precoder of claim 9, wherein C=MR denotes QR decomposition(QRD) of C, M being a unitary matrix, and R being an upper righttriangular matrix; wherein the feedforward filter matrix F isF=Diagonal(R); and wherein the interference pre-cancellation matrix G isG=FR^(†), where superscript † denotes a Moore-Penrose GeneralizedInverse.
 11. The GDFE precoder of claim 7, further comprising: a modulounit disposed in the feedforward path to produce a stream of filteredvector symbols X which are fed back through the interferencepre-cancellation block disposed in the feedback path.
 12. The GDFEprecoder of claim 11, wherein an output signal of the interferencepre-cancellation block is subtracted from a stream of user symbols andapplied to the modulo unit in the feedforward path.
 13. The GDFEprecoder of claim 12, further comprising: a transmit filter representedby the transmit filter matrix B for filtering the stream of filteredvector symbols X produced by the modulo unit disposed in the feedforwardpath; wherein the transmit filter matrix B isB=VΣ^(1/2)M.
 14. A MU-MIMO wireless system comprising: a base stationincluding the GDFE precoder of claim 13; a plurality of K userterminals; and a channel, represented by the DL channel matrix H throughwhich communications occur in the wireless system with the userterminals, to receive an output of the transmit filter.
 15. Ageneralized decision feedback equalizer (GDFE) based precoder in a basestation (BS) of a multi-user multiple-input multiple-output (MU-MIMO)wireless system having K user terminals (UTs) which communicate with thebase station via an uplink (UL) channel and a corresponding downlink(DL) channel, the GDFE precoder comprising: a decision feedbackequalizing stage for processing user symbols to produce filtered vectorsymbols, the decision feedback equalizing stage including aninterference pre-cancellation stage having an interferencepre-cancellation matrix G used in a transmitter at the interferencepre-cancellation stage; and a transmit filter represented by a transmitfilter matrix B for processing the filtered vector symbols after thedecision feedback equalizing stage to produce an output of transmittedsignals to be directed to the DL channel represented by the effective DLchannel matrix H through which communications occur in the wirelesssystem with the user terminals; wherein the interferencepre-cancellation matrix G is computed based on a feedforward filtermatrix F and a filter matrix C, the feedforward filter matrix F iscomputed based on the filter matrix C, the filter matrix C is computedbased on an uplink (UL) covariance matrix D, the UL covariance matrix Dis computed by assuming there are as many user terminals as a number ofrows in an effective downlink (DL) channel matrix H, the UL covariancematrix D is a diagonal matrix, and the effective DL channel matrix H isobtained after receiver processing at the user terminals; wherein theeffective downlink (DL) channel matrix isH=[Ĥ₁ ^(H), Ĥ₂ ^(H), . . . , Ĥ_(K) ^(H)] where Ĥ_(k) is an effective DLchannel sub-matrix for the k^(th) UTĤ_(k)=S_(k)V_(k) ^(H). where S_(k) and V_(k) are matrices obtained froma singular value decomposition (SVD) of an estimated DL channel matrixH_(k) for the k^(th) UTH_(k)U_(k)S_(k)V_(k) ^(H).
 16. The GDFE precoder of claim 15, whereinU_(k) ^(H) is used for receiver processing at the k^(th) UT and theeffective DL channel sub-matrix for the k^(th) UT, Ĥ_(k), is provided tothe base station by the k^(th) UT.
 17. The GDFE precoder of claim 15,whereinC=[√{square root over (Σ^(†))}−λ√{square root over (Σ)}]V ^(H) H ^(H) D,where superscript † denotes a Moore-Penrose Generalized Inverse, andwhere V is a unitary matrix and Σ is a diagonal matrix with non-negativeentries in an Eigen Value Decomposition (EVD) of an input covariancematrix S_(xx) represented asS_(xx)=VΣV^(H), and λ is a UL/DL duality variable for a given totaltransmit power P_(t),λ=trace(I−[H _(DL) ^(H) DH _(DL) +I] ⁻¹)/P _(t), where V is a unitarymatrix and Σ is a diagonal matrix with non-negative entries, and theinput covariance matrix S_(xx) is computed as$S_{xx} = {{V\; \Sigma \; V^{H}} = {\frac{I - \left\lbrack {{H_{DL}^{H}{DH}_{DL}} + I} \right\rbrack^{- 1}}{\lambda}.}}$18. The GDFE precoder of claim 17, wherein C=MR denotes QR decomposition(QRD) of C, M being a unitary matrix, and R being an upper righttriangular matrix; wherein the feedforward filter matrix F isF=Diagonal(R) ; and wherein the interference pre-cancellation matrix GisG=FR^(†), where superscript † denotes a Moore-Penrose GeneralizedInverse.
 19. The GDFE precoder of claim 15, wherein the decisionfeedback equalizing stage includes a modulo unit disposed in afeedforward path to produce a stream of filtered vector symbols X whichare fed back through an interference pre-cancellation block disposed ina feedback path, the interference pre-cancellation block denoted by I−Gdisposed in the feedback path, wherein an output signal of theinterference pre-cancellation block is subtracted from a stream of usersymbols and applied to the modulo unit in the feedforward path.
 20. AMU-MIMO wireless system comprising: a base station including the GDFEprecoder of claim 15; a plurality of K user terminals; and a channel,represented by the effective DL channel matrix H through whichcommunications occur in the wireless system with the user terminals, toreceive the output of the transmit filter.